I am looking to get from the Farmers Market at PSU to the SWCC (6820 SW 45th Ave). I am really unfamiliar with biking on the westside, particularly in SW PDX. I'll be trailing by daughter on a tag-along and also will have a visiting friend riding with me too. So, we're looking for the safest route possible. I bycycle'd it, but I'm looking for first-hand experience with riding areas like Terwilliger or Capitol Hwy.

Since you say you have ridden this route, I'm unclear on just what you are trying to find out, but I'll give you my take:
I live in Hillsdale. The obvious route from PSU to the SWCC is straightforward: Broadway->Terwilliger->Capitol Hwy->Vermont. The hairy portion is the transition from Terwilliger onto Capitol Highway and to the Beaverton-Hillsdale Hwy split. You are riding through the commercial part of Hillsdale, and, to stay on Capitol Hwy you have to ride in the left-hand lane. This section of the highway can be nasty, with lots of curb cuts, drivers turning right and left, and impatient commuters speeding toward Beaverton. I personally would not feel comfortable trailering a child through this. It's scary enough as a single adult rider.
Unfortunately, I don't have a better route to suggest. Everything I conceive of has its own drawbacks--and would be longer. Perhaps TriMet isn't such a bad idea. Sorry.

I used to live in this area and here's how I'd do it (if I was pulling a trailer):
Broadway -> Terwilliger -> Barbur (right turn) -> Bertha Blvd (right turn) -> Vermont (left turn, ready to climb a hill now?) -> Capitol Hwy (left turn) -> Vermont (again, where Capitol Hwy veers to the left, stay straight). Now you just stay on Vermont to the bottom of the hill, past Gabriel Park to the SWCC. This is a bit longer than the previous route recommended, but it avoids the stress of Capitol Hwy from Terwilliger through Hillsdale. The worst part is a short stretch of Vermont past 30th Avenue to around 34th, where there is little to no shoulder, but I've found traffic to be cooperative here.

Returning it's a long uphill haul back up Vermont, but just reverse the route. If you prefer you can return via Barbur Blvd (and bypass the challenging left turn onto Terwilliger from Barbur) to downtown (to Naito or 4th Ave).